The present invention relates to optical systems capable of performing linear mathematical functions. More particularly, the invention relates to improvements in the form of an optical mask which is used in such systems to represent a known two-dimensional matrix having both positive and negative elements. The apparatus of the invention is specifically designed to permit the multiplication of a bipolar matrix which is represented by a single optical mask.
Characteristically, optical computing systems operate by directing one or more beams of light through an optical material of variable transmittance. The intensity of a light beam is adjusted to represent a predetermined value, while the transmittance of the material is altered to indicate another predetermined value. A solution for an equation containing the two predetermined values is obtained by observing the intensity of the beam after it passes through the optical material.
Conventionally, the optically transmissive material is in the form of a mask having selectively variable optical characteristics which enable one to program or select varying values of transmittance. Further, it is known to divide the area of such a mask into a number of zones of independently selectable transmittance so that the mask can represent a plurality of separate values, with the transmittance of each zone representing a respective value. Examples of such systems for optically performing mathematical computations are shown in the following U.S. Pat. Nos.: 4,286,382; 3,042,912; 3,068,361; and 3,937,942.
As is known, an optical computing system can efficiently perform matrix operations when the mask is subdivided into a plurality of separate zones as described above, and the zones are arranged in rows and columns to form a two-dimensional matrix. Characteristically, one or more such masks are disposed to intercept a number of light beams. In operation, the light beams can represent a matrix of values, with each beam indicating a respective value of the matrix. After passage through the mask or masks, the beams are separately detected by one or more photodetectors and converted thereby into electrical signals representative of the product of two or more matrices. Examples of optical computing systems employing optically-encoded masks to perform matrix multiplication are found in U.S. Pat. No. 3,305,669; U.S. Pat. No. 3,588,486; U.S. Pat. No. 4,009,380; and in an article entitled "Optical Matrix Inverter," by G. Fan, which appeared in IBM Technical Disclosure Bulletin, Vol. VI, No. 1, June 1963. In addition, U.S. Pat. No. 4,386,414 discloses the use of a mask consisting of a holographic optical element which is subdivided into an M.times. N element matrix.
An important limitation of the optical matrix multiplication systems described or disclosed in the cited references is their inability to operate with bipolar values. As is known, light, unlike electricity, can be expressed only in unipolar quantities. Hence, without some provision in the optical system for representing and manipulating negative values, the disclosed matrix multipliers are limited to use with only unipolar values.
Two examples of optical computing systems which do provide for the manipulation of bipolar values are U.S. Pat. No. 2,702,158 and U.S. Pat. No. 2,712,415. In the first example, mathematical functions are performed by providing electrical signals representative of selected values to respective sweep circuits of a conventional cathode ray tube. The sweep circuits are configured to perform a predetermined mathematical function with values represented by the applied signals, and the screen of the tube is divided into four quadrants into which the tube's beam can be deflected. Each quadrant is representative of the sign of the solution of the function with voltages of selected magnitude and polarity applied to the CRT's sweep circuits. In U.S. Pat. No. 2,712,415, an optical computer is adapted to manipulate two functions irrespective of their signs by the provision of separate areas on one or more coded optical masks. Each area is representative of the positive or negative portion of a respective function, and the system transmits one beam of light through all positive portions of all functions and a separate beam through the negative portions of all functions. The beams are detected and combined to provide the algebraic product of the functions. Neither of these examples provide a suitable means for operating in combination with an encoded mask upon which representation of bipolar values have been randomly distributed.
The following references are of general interest to the field of optical computing: U.S. Pat. No. 2,740,583; U.S.S.R. Disclosure No. 690,509; U.S.S.R. Disclosure No. 660,065; and French Patent No. 1,246,536.